Here, there are confusions, things we can answer and things which we cannot.
Greeks and Egyptians
Both Greeks and Egyptians are civilizations from the antique time. But:
- Egypt runs from 3000 BC (yeah this is OLD) and disappears in 3O BC with Cleopatra VII Philator (THE Cleopatra). Egypt will know 3 different eras (old/Middle/new Kindom) and different levels of power. Egypt is at its apogee during the New Kingdom and will then slowly fall. Roughly 1000 BC representc the time Egypt stops doing anything significant. Note that Egypt is conquered by the Persian and then Greeks (Cleopatra being a Ptolemy IS Greek).
- Greece is a baby. We can't say anything of Greece before 800 BC but Greece really starts to shine in 500 BC.
You can see here something: Egypt and Greece while both of the antique time does not exactly coincide with two things:
- The moment they start to shine
- The length of that shining
Second point. At the moment Greece is starting to shine, the dominant civilization is Persia. And the relation between Greece and Persia is relatively more important that between Greece and Egypt. This is illustrated by the "Medic war" when King Xerxes tried to invade Greece and got his butt severely kicked (you have a fairly naive representation of that in the comic/movie 300)
It appears so that the Greeks we know (read Herodotus, Thucydides, Plato, Euripides [especially his Persia]) and you will see the Greeks dancing on their foot regarding Persians. Herodotus gives, for example, a fairly accurate description of Egypt (with his usual fantasy), but concerning his subject, Persian, try to count the number of time he is mentioning Persepolis (0 times in case you don't know). So Greeks tend naturally to project themselves with Egypt, but rightfully a lot of their culture was from East. Their writing system and lots of their legends are rooted in the Near East much more than Egypt.
The Egyptians God's head
this is the kind of question which is unanswerable. Not much more than explaining to you why Rembrandt while using so few light and Picasso was breaking his subject, either than: because they did... There is theory here and there about that: psychoanalysis, psychology, philosophy, extraterrestrials, if you are interested look for them.
Now generally Egyptian painting is a little bit hard to understand for the modern standard we are just living with it "culturally". Knowing why their gods have an animal head makes as sense as trying to understand why the Hell all their humans' head are looking on the side when their statues are so fairly accurate... Because they did...
Factually yes there is... Numerous gods were represented with a purely human form. And amusingly you can know them. This is, for example, Neith:
More amusingly without looking for Neith (I cited here because of Smite... modern video game with success), Isis, Osiris are human faced.
BUT it is slightly much more complex than that:
This is the tablet of Narmer, representing the Predynastic King Narmer unifying the Upper and Lower Egypt. Significantly for your question, you can see 2 things:
- the falcon, traditionally linked with the Pharaoh as Horus, so almost without question, that falcon IS Horus, his hieroglyph is a falcon + a trait (the trait simply means it is a subject, here the falcon god)
- Up to the tablet, you have a bull/cow's head, another fairly traditional god in Egypt, Hathor, once again represented as an animal
Now you see, that Horus is possessing:
- a purely falcon form (called theriomorphic form), generally predynastic, Old Kingdom
- the usual form you know from him: human body, falcon head (called therianthropic form), generally old Kingdom up to new Kingdom
- a purely human form (yes), with generally him as a child and Isis holding him (and yes it looks a lot like "madonna's illustrations of Christians... yes it does), generally Ptolemy's time
Those forms do not necessarily are present at the same moment in history but you have now a complete picture of Egyptian Gods.
The sphinx is one of the only representation of the other therianthropic form, human head, animal body. Note there is a lot of sphinx in Egypt they are highly praised during the New Kingdom and decorate mostly the tombs to guard them either as Lion body + human head, or falcon, panther, jackal (the one on Tuthankamon tomb was a jackal) etc.